Development of Co-Rich Microwires with Graded Magnetic Anisotropy

In this paper, a gradual change in the hysteresis loop of Co-rich glass-coated microwire stress-annealed at variable temperature is observed. Such microwires annealed with a temperature gradient also present a variable squareness ratio and magnetic anisotropy field along the microwire’s length. The obtained graded anisotropy has been attributed to a gradual modification of the domain structure along the microwire originated by a counterbalance between shape, magnetoelastic, and induced magnetic anisotropies. Accordingly, we propose a rather simple route to design graded magnetic anisotropy in a magnetic microwire.

One of the general issues of traditional soft magnetic materials (e.g., Permalloy, Fe-Si, ferrites) is that their magnetic softness is substantially affected by processing. Accordingly, in most crystalline soft magnetic materials, a specially designed sequence of thermal treatments (including hot and cold rolling, annealing at carefully selected conditions (atmosphere, temperature), recrystallization) is needed to achieve good magnetic softness [1].
In the absence of magnetocrystalline anisotropy, shape anisotropy, and magnetoelastic anisotropy play a decisive role in the formation of the magnetic properties of amorphous materials. The best magnetic softness of amorphous materials can be generally Therefore, magnetic properties of amorphous materials are affected by the fabrication conditions (like quenching rate or internal stresses value and distribution) as well as by the chemical composition of the metallic alloy [18,[22][23][24].
Additionally, the magnetic softness of amorphous materials is affected by a number of factors, like surface irregularities, intrinsic fluctuations of exchange energies and local anisotropies, clusters and chemical short-ordered regions, and relaxation effects due to local structural rearrangements linked to the fabrication process and post-processing [25,26].
In soft magnetic materials with cylindrical symmetry and thin dimensions, the magnetization can be oriented along the long wire axis. Therefore, amorphous wires can present peculiar magnetic properties, like so-called magnetic bistability characterized by perfectly rectangular hysteresis loops [27][28][29][30].
The so-called Taylor-Ulitovsky technique allows for magnetic wires of the widest diameter range to be manufactured (from 200 nm up to 100 µm), coated with an insulating and flexible glass coating [36][37][38].
An important advantage of the Taylor-Ulitovsky technology is that the wire diameter can be significantly reduced (usually by an order of magnitude). This diameter reduction is especially important for applications of magnetically bistable wires, since perfectly rectangular hysteresis loops can be observed only for wires with a minimum length [27,39].
Another advantage of glass-coated microwires is better corrosion resistance and (in some cases) mechanical properties provided by flexible, thin, biocompatible, and insulating glass coating. Such peculiarities of glass-coated microwires make them suitable for completely new applications, including biomedicine, non-destructive control of external stimuli (stress, temperature) in smart composites with microwire inclusions, magnetic memories and logics, magnetic and magnetoelastic sensors, or electronic surveillance [4,7,[18][19][20][40][41][42].
Recently, substantial increases in H c and M r /M o have been reported upon conventional furnace annealing of Co-rich microwires, while magnetic softness (decrease in H c , M r /M o , GMI ratio, H k ) can be significantly improved by stress annealing [47][48][49].
While in the case of Co-rich stress-annealed microwires, the study of magnetic anisotropy has not been fully explored, in the case of Co-rich amorphous ribbons, stress-annealinginduced magnetic anisotropy and its influence on the off-diagonal GMI effect has already been reported and used for the construction of GMI sensors [50,51].
On the other hand, stress-annealing-induced magnetic anisotropy has been reported for Fe-rich microwires with positive λ s [44,52]. Additionally, the dependence of stressannealing-induced magnetic anisotropy in Fe-rich microwires on annealing temperature has been proposed for the development of graded magnetic anisotropy [53]. The said graded magnetic anisotropy is obtained by a rather simple method consisting of annealing at fixed applied stress and a variable annealing temperature. Previously, graded magnetic anisotropy was obtained by a rather sophisticated method involving modification of the chemical composition during the sample preparation [54,55]. Magnetic materials with graded magnetic anisotropy presenting controllable spatial distribution of the magnetic anisotropy can show unusual magnetic properties: it was predicted [56] and recently experimentally shown [53,57] that materials with graded magnetic anisotropy can present controllable nucleation or pinning of domain walls.
The common features of Fe-and Co-rich microwires is that stress-annealing-induced anisotropy in both materials (Fe-and Co-rich microwires) is affected by several parameters, like T ann , t ann , σ [47][48][49][50][51][52][53]. Recently, it was observed that such stress-annealing in Fe-rich microwires is only partially reversible: subsequent annealing can recover only part of the stress-annealing-induced anisotropy [58,59]. Additionally, the said induced magnetic anisotropy is proportional to the T ann , t ann , σ-that is, the induced anisotropy increases when the T ann is increased under constant t ann and/or σ [58]. Accordingly, the parameter that can be modified during stress-annealing in the easiest way is T ann . Therefore, stressannealing in a T ann gradient was proposed for the development of Fe-rich microwires with graded magnetic anisotropy [53,57].
Considering that, similarly to Fe-rich microwires, stress-annealing-induced magnetic anisotropy of Co-rich microwires is affected by T ann , t ann , σ, we intend to extend our studies to Co-rich microwires with the aim of developing Co-rich microwires with graded magnetic anisotropy. Accordingly, in this paper, we present our recent experimental results on the preparation and processing of Co-rich magnetic microwires with graded magnetic anisotropy. Such graded magnetic anisotropy has been obtained by stress-annealing of Co-rich microwires at variable annealing temperatures.

Materials and Methods
Studied Co-rich glass-coated microwires have been prepared using the Taylor-Ulitovsky technique involving rapid melt quenching of metallic alloys covered by an insulating glass shell. The details of the preparation technique are described elsewhere [35][36][37]. We studied Co 64 Both microwires present excellent magnetic softness with coercivities, H c , 14, and 3 A/m and magnetic anisotropy fields, H k , 100, and 40 A/m, respectively, typical for amorphous materials (see Figure 1).
Both microwires present excellent magnetic softness with coercivities, Hc, 14, and 3 A/m and magnetic anisotropy fields, Hk, 100, and 40 A/m, respectively, typical for amorphous materials (see Figure 1). Hysteresis loops in as-prepared and annealed samples were measured using the fluxmetric method detailed elsewhere [48]. For a better comparison of samples with different composition and geometry and subjected to different heat treatments, the hysteresis loops are presented as the dependence of the normalized magnetization, M/M0, (where M is the magnetization in a given magnetic field, and M0 is the magnetization in the maximum applied field) on the magnetic field, H. The magnetic field is created by a long (about 12 cm long) and thin (about 8 mm in diameter) solenoid. As described elsewhere, the magnetic field generated by such a solenoid is fairly uniform along the axis over a sufficiently long (about 90% of the solenoid length) region [60,61].
The hysteresis loops of samples as-prepared and stress-annealed at a constant temperature were measured using a pick-up coil that was 20 mm long. In this case, the sample length was 50 mm, and each sample was placed inside the solenoid which was 120 mm long. The variation of the hysteresis loops along the sample length was evaluated using a short (2 mm long), movable pick-up coil, as also recently reported for Fe-rich microwires [57]. In both cases, it is essentially relevant that the pick-up coil lengths (2 mm and 20 mm, respectively) are much shorter than the length of the magnetizing coil (120 mm). Therefore, the sample is magnetized by a rather uniform magnetic field at the sample portion where the magnetization is measured by the pick-up coils.
It is worth mentioning that, usually, the Taylor-Ulitovsky technique is employed for preparation of thinner microwires (typically with diameters, d, of a metallic nucleus below 50 μm). However, recent preparation of Fe-rich glass-coated microwires with d ≥ 100 μm was reported [38]. Such "thick" microwires present certain interest for industrial applications, like non-contact stress monitoring or magnetic tags [18,40]. The magnetic properties of "thick" Fe-rich glass-coated microwires are rather different from those of thinner Fe-rich glass-coated microwires [38]. Therefore, for the present studies, we have selected two Co-rich microwires with fairly similar compositions, but with rather different d-values.
Both samples were annealed in a standard Thermolyne furnace. The annealing at variable temperature was performed in a similar way as for Fe-rich microwires [57]: a 30 Hysteresis loops in as-prepared and annealed samples were measured using the fluxmetric method detailed elsewhere [48]. For a better comparison of samples with different composition and geometry and subjected to different heat treatments, the hysteresis loops are presented as the dependence of the normalized magnetization, M/M 0 , (where M is the magnetization in a given magnetic field, and M 0 is the magnetization in the maximum applied field) on the magnetic field, H. The magnetic field is created by a long (about 12 cm long) and thin (about 8 mm in diameter) solenoid. As described elsewhere, the magnetic field generated by such a solenoid is fairly uniform along the axis over a sufficiently long (about 90% of the solenoid length) region [60,61].
The hysteresis loops of samples as-prepared and stress-annealed at a constant temperature were measured using a pick-up coil that was 20 mm long. In this case, the sample length was 50 mm, and each sample was placed inside the solenoid which was 120 mm long. The variation of the hysteresis loops along the sample length was evaluated using a short (2 mm long), movable pick-up coil, as also recently reported for Fe-rich microwires [57]. In both cases, it is essentially relevant that the pick-up coil lengths (2 mm and 20 mm, respectively) are much shorter than the length of the magnetizing coil (120 mm). Therefore, the sample is magnetized by a rather uniform magnetic field at the sample portion where the magnetization is measured by the pick-up coils.
It is worth mentioning that, usually, the Taylor-Ulitovsky technique is employed for preparation of thinner microwires (typically with diameters, d, of a metallic nucleus below 50 µm). However, recent preparation of Fe-rich glass-coated microwires with d ≥ 100 µm was reported [38]. Such "thick" microwires present certain interest for industrial applications, like non-contact stress monitoring or magnetic tags [18,40]. The magnetic properties of "thick" Fe-rich glass-coated microwires are rather different from those of thinner Fe-rich glass-coated microwires [38]. Therefore, for the present studies, we have selected two Co-rich microwires with fairly similar compositions, but with rather different d-values.
Both samples were annealed in a standard Thermolyne furnace. The annealing at variable temperature was performed in a similar way as for Fe-rich microwires [57]: a 30 cm long microwire was annealed in a conventional furnace under tensile stress, σ, created by a mechanical load, P, attached to one end of the microwire (see Figure 2). Such σ-magnitude was obtained considering the composite structure of microwires consisting of a metallic nucleus and glass coating with different Young moduli (E 2 -for the metal and E 1 -for the glass coating), as previously described elsewhere [49][50][51][52][53]58]: being K = E 2 /E 1 and S m and S gl being the metallic nucleus and glass coating cross-sections, respectively.
being K = E2/E1 and Sm and Sgl being the metallic nucleus and glass coating cross-sections, respectively.
In fact, for a more correct estimation of E2 and E1 values during stress-annealing, it is necessary to consider E2 and E1 values at the annealing temperature. Additionally, it is more correct to consider E2 values for amorphous alloys (not for pure metals).
A decrease in both E2 and E1 upon heating was experimentally observed [63,64]. From the experimentally measured E2 and E1 temperature dependencies [63,64], the following E-values can be considered: E2 = 14,500 kg/cm 2 [63] and E1 = 7400 kg/cm 2 [64]. Although these E2 and E1-values are different from those previously considered [49][50][51]60], the K-coefficient given as E2/E1 remains the same: K = E2/E1 ≈ 2. For the present case, σ ≈ 500 MPa and 400 MPa were used for samples 1 and 2, respectively. One end of the studied microwire was introduced into the furnace through the orifice up to the zone with constant temperature, T, while the opposite sample end remained outside the furnace. Like in any real furnace, there is a zone with constant T, in the middle of the furnace, while near the ends the temperature is more general, and hence, a temperature gradient exists near the ends of the furnace [65].
The temperature distribution, measured using a commercial (NiCr-Ni) thermocouple (when T is set to 300 °C) inside the furnace, in the orifice (through which the microwire is introduced into the furnace) and near the furnace is shown in Figure 3. Consequently, part of the sample placed in the zone with constant T was stress-annealed at a fixed temperature and part of the sample placed in the temperature gradient zone was stress-annealed under variable T. In previous publications [49][50][51]62], Young moduli at room temperature for pure metal (E 2 = 1.5 × 10 11 Pa) and Pyrex glass (E 1 = 7.5 × 10 10 Pa) were used for stresses estimation. Accordingly, the coefficient K = E 2 /E 1 ≈ 2 was used.
In fact, for a more correct estimation of E 2 and E 1 values during stress-annealing, it is necessary to consider E 2 and E 1 values at the annealing temperature. Additionally, it is more correct to consider E 2 values for amorphous alloys (not for pure metals).
One end of the studied microwire was introduced into the furnace through the orifice up to the zone with constant temperature, T, while the opposite sample end remained outside the furnace. Like in any real furnace, there is a zone with constant T, in the middle of the furnace, while near the ends the temperature is more general, and hence, a temperature gradient exists near the ends of the furnace [65].
The temperature distribution, measured using a commercial (NiCr-Ni) thermocouple (when T is set to 300 • C) inside the furnace, in the orifice (through which the microwire is introduced into the furnace) and near the furnace is shown in Figure 3. Consequently, part of the sample placed in the zone with constant T was stress-annealed at a fixed temperature and part of the sample placed in the temperature gradient zone was stress-annealed under variable T.
Finally, the microwire placed outside the furnace was just loaded and unloaded. The presence of an insulating glass-coating allows for annealing of microwires in air. Similar stress-annealing conditions (T ann , σ) were used in previous publications [47][48][49]. The integrity of microwires before and after stress-annealing was checked by optical microscopy.  Finally, the microwire placed outside the furnace was just loaded and unloaded. The presence of an insulating glass-coating allows for annealing of microwires in air. Similar stress-annealing conditions (Tann, σ) were used in previous publications [47][48][49]. The integrity of microwires before and after stress-annealing was checked by optical microscopy.
One of the most important advantages of amorphous materials is better mechanical properties (e.g., high ductility). Therefore, we chose an annealing temperature, Tann, (300 °C) well below the crystallization temperature. In previous publications, the most significant change in magnetic anisotropy for selected Tann in Co-rich microwires was observed at σ ≈ 350 MPa [47][48][49]. Correspondingly, the mechanical load was selected, allowing to apply σ ≈ 400 and 500 MPa.
The crystallization, Tcr, and Curie, Tc, temperatures of the studied microwires, evaluated by the DSC method as described elsewhere [66], were about 510 and 370 °C, respectively. Tcr and Tc, values are consistent with the values observed in CoFeCrSiB microwires [46] and ribbons [67,68] with similar compositions. Consequently, like other Co-rich stress-annealed microwires, the studied microwires annealed at Tann ≤ 300 °C retain amorphous structure after stress-annealing [47][48][49]. The amorphous structure of stress-annealed microwires is also indirectly confirmed by the excellent magnetic softness (see Figure 4) and ductility typical for amorphous materials-substantial magnetic hardening has been reported elsewhere at the onset of crystallization [67]. One of the most important advantages of amorphous materials is better mechanical properties (e.g., high ductility). Therefore, we chose an annealing temperature, T ann , (300 • C) well below the crystallization temperature. In previous publications, the most significant change in magnetic anisotropy for selected T ann in Co-rich microwires was observed at σ ≈ 350 MPa [47][48][49]. Correspondingly, the mechanical load was selected, allowing to apply σ ≈ 400 and 500 MPa.
The crystallization, T cr , and Curie, T c , temperatures of the studied microwires, evaluated by the DSC method as described elsewhere [66], were about 510 and 370 • C, respectively. T cr and T c , values are consistent with the values observed in CoFeCrSiB microwires [46] and ribbons [67,68] with similar compositions. Consequently, like other Co-rich stress-annealed microwires, the studied microwires annealed at T ann ≤ 300 • C retain amorphous structure after stress-annealing [47][48][49]. The amorphous structure of stress-annealed microwires is also indirectly confirmed by the excellent magnetic softness (see Figure 4) and ductility typical for amorphous materials-substantial magnetic hardening has been reported elsewhere at the onset of crystallization [67].

Experimental Results and Discussion
• Dependence of hysteresis loops on stress-annealing conditions; • Variation of magnetic properties along the wires associated with temperature gradients during stress-annealing.
A modification of the hysteresis loops of studied samples was observed upon stressannealing (see Figure 4). As mentioned above, the hysteresis loops of Co-rich microwires with vanishing λs-values are usually substantially affected by stress-annealing [42,47,48].
Thus, an almost anhysteretic loop with Hk ≈ 900 A/m is observed in sample 1 stress-annealed at Tann = 300 °C (see Figure 4a). Such a character of the hysteresis loop

•
Dependence of hysteresis loops on stress-annealing conditions; • Variation of magnetic properties along the wires associated with temperature gradients during stress-annealing. A modification of the hysteresis loops of studied samples was observed upon stressannealing (see Figure 4). As mentioned above, the hysteresis loops of Co-rich microwires with vanishing λ s -values are usually substantially affected by stress-annealing [42,47,48].
Thus, an almost anhysteretic loop with H k ≈ 900 A/m is observed in sample 1 stressannealed at T ann = 300 • C (see Figure 4a). Such a character of the hysteresis loop must be attributed to a transverse character of stress-annealing-induced magnetic anisotropy and magnetization processes by magnetization rotation. The opposite tendency is observed for sample 2: the hysteresis loop becomes almost perfectly rectangular with H c ≈ 11 A/m (see Figure 4b).
In these experiments, we used the same T ann , and t ann , while σ-magnitudes evaluated from Equation (2) were 500 and 400 MPa. Therefore, the observed difference in the effect of stress-annealing on hysteresis loops of studied samples (see Figure 4a,b) can be attributed to different σ-magnitudes. As recently reported [53], even in the same Co-rich microwire, the stress-annealing-induced anisotropy is considerably affected by the σ-values: in Fe 3.6 Co 69.2 Ni 1 B 12.5 Si 11 Mo 1.5 C 1.2 microwires for σ ≥ 470 MPa, the character of the induced anisotropy changed from axial to transverse [53]. Alternatively, λ s is affected by stresses (either applied or internal) [69]. Such stress-dependence of λ s can be essentially relevant for Co-rich amorphous materials with vanishing λ s . Therefore, annealing can affect not only the λ s -value, but even its sign [52]. Accordingly, observed differences of hysteresis loops in both stress-annealed samples can also be related to different chemical compositions, and hence to λ s -values.
As recently shown, the stress-annealing-induced magnetic anisotropy of microwires depends on T ann , t ann , and σ [53,57,70]. Accordingly, stress-annealing of Fe-rich microwires in the T ann gradient was employed for realization of controllable spatial distribution of the magnetic anisotropy, that is, for development of graded magnetic anisotropy [53,57].
Below, we use the same concept for studied Co-rich microwires. Similarly to previous publications on graded anisotropy in Fe-rich microwires, we used the dependence of the stress-annealing-induced anisotropy on the annealing temperature, T ann [53,57,70].
As shown in Figures 5 and 6, a gradual change in the hysteresis loop (measured by the short pick-up coil) of both samples stress-annealed at variable T ann is observed. Thus, we can deduce that sample 1 presents variable remanent magnetization, Mr/M0, and a magnetic anisotropy field, Hk, along the microwire length, L (see Figure 7a,b). Both samples present variation of their magnetic properties along their lengths associated with the T ann gradient produced during stress-annealing (see Figures 5 and 6). Thus, we can deduce that sample 1 presents variable remanent magnetization, M r /M 0 , and a magnetic anisotropy field, H k , along the microwire length, L (see Figure 7a,b).  Similarly, a modification in the remanent magnetization, Mr/M0, and the coercivity, Hc, is observed in sample 2 subjected to stress-annealing in the Tann gradient (see Figure  8).
Generally, the evolution of magnetic properties upon stress-annealing in Tann gradients observed in both samples presents features similar to the ones already reported for stress-annealing-induced magnetic anisotropy in Co-rich microwires [47][48][49]. Thus, from a comparison of Figures 3, 7a, and 8a, we can deduce an increase in Mr/M0 followed by a   Similarly, a modification in the remanent magnetization, M r /M 0 , and the coercivity, H c , is observed in sample 2 subjected to stress-annealing in the T ann gradient (see Figure 8). It should be noted that the experimental data were obtained in different conditions: (i) Co69.2Fe3.6Ni1B12.5Si11Mo1.5C1.2 microwires studied in the Refs. [47][48][49] were annealed each time at different temperatures, with the sample being placed in the furnace zone with stable T. On the other hand, samples 1 and 2 were placed into the furnace zone with variable T, and therefore a Tann spectrum from room temperature to 300 °C can be realized in the same sample. Generally, the evolution of magnetic properties upon stress-annealing in T ann gradients observed in both samples presents features similar to the ones already reported for stress-annealing-induced magnetic anisotropy in Co-rich microwires [47][48][49]. Thus, from a comparison of Figures 3, 7a and 8a, we can deduce an increase in M r /M 0 followed by a decrease with increasing T ann in both samples. Additionally, almost anhysteretic loops with high enough H k , observed in the sample 1 portion subjected to stress-annealing at sufficiently high T ann must be attributed to transverse magnetic anisotropy and remagnetization by magnetization rotation.
An attempt to compare M r /M 0 (T ann ) and H c (T ann ) dependencies evaluated from Figures 5-8 and similar dependencies previously reported for the Co 69.2 Fe 3.6 Ni 1 B 12.5 Si 11 Mo 1.5 C 1.2 microwire is provided in Figure 9.
It should be noted that the experimental data were obtained in different conditions: (i) Co 69.2 Fe 3.6 Ni 1 B 12.5 Si 11 Mo 1.5 C 1.2 microwires studied in the Refs. [47][48][49] were annealed each time at different temperatures, with the sample being placed in the furnace zone with stable T. On the other hand, samples 1 and 2 were placed into the furnace zone with variable T, and therefore a T ann spectrum from room temperature to 300 • C can be realized in the same sample. (ii) Although all Co-rich microwires present vanishing λ s -values, even as-prepared samples have different hysteresis loops. Such difference can be attributed to slightly different chemical compositions and different geometries. (iii) Additionally, the stress, σ, applied during annealing under mechanical load, evaluated by Equation (2), is different for all studied microwires due to different dand D-values.
Accordingly, the as-prepared Co 69.2 Fe 3.6 Ni 1 B 12.5 Si 11 Mo 1.5 C 1.2 microwire studied in refs. [47][48][49] presents lower M r /M 0 and H c -values than samples 1 and 2. However, despite the aforementioned differences, there are a few common features. Thus, an increase in M r /M o versus T ann is observed in the Co 69.2 Fe 3.6 Ni 1 B 12.5 Si 11 Mo 1.5 C 1.2 microwire, annealed at σ ≈ 354 MPa, and in sample 2, annealed at σ ≈ 400 MPa (see Figure 9a). However, the M r /M o (T ann ) dependence for a Co 69.2 Fe 3.6 Ni 1 B 12.5 Si 11 Mo 1.5 C 1.2 microwire annealed at σ ≈ 472 MPa shows a slight increase followed by a decrease in M r /M o . Similarly, a decrease in M r /M o versus T ann is observed for sample 1 annealed at σ ≈ 500 MPa (see Figure 9a). From the provided comparison, it can be deduced that there is a general tendency toward a decrease in M r /M o upon annealing at sufficiently high T ann and σ. It should be noted that the experimental data were obtained in different conditions: (i) Co69.2Fe3.6Ni1B12.5Si11Mo1.5C1.2 microwires studied in the Refs. [47][48][49] were annealed each time at different temperatures, with the sample being placed in the furnace zone with stable T. On the other hand, samples 1 and 2 were placed into the furnace zone with variable T, and therefore a Tann spectrum from room temperature to 300 °C can be realized in the same sample. Some tendency can also be extracted from the H c (T ann ) dependencies. Thus, for a Co 69.2 Fe 3.6 Ni 1 B 12.5 Si 11 Mo 1.5 C 1.2 microwire annealed at σ ≈ 354 MPa, an increase in H c (T ann ) is observed, followed by a decrease (Figure 9b), while a decrease in H c is observed in sample 1 annealed at σ ≈ 500 MPa (see Figure 9b).
On the other hand, saturation magnetization of both samples remains almost unchanged: magnetic moment values evaluated by measurements at H = 1T (using VSM magnetometer) were almost the same. Such features of stress-annealed samples must be attributed to the amorphous structure of as-prepared and all stress-annealed samples. Indeed, the influence of annealing on saturation magnetization can be relevant upon devitrification of the amorphous precursor [71]. However, in amorphous materials, the saturation magnetization value is determined by the chemical composition [22]. It is generally accepted and even experimentally proved that the saturation magnetization of amorphous materials is almost independent of annealing [72].
Differences between the two studied samples must be attributed to (i) different λ svalues (as their chemical compositions are different) and (ii) different σ-values (500 MPa and 400 MPa, respectively).
The modification of the hysteresis loops of the studied microwires must be related to the magnetic domain structure of microwires, which is affected by the λ s -value and sign, the internal stresses distribution, and the shape magnetic anisotropy. Thus, the axial magnetization alignment promoted by the exchange energy contribution is especially relevant for the case of thin and long enough magnetic wires due to high shape anisotropy [27,73,74]. However, in Co-rich magnetic microwires with λ s < 0, the presence of internal stresses is another factor that affects magnetoelastic anisotropy, K me given by Equation (1).
Consequently, the counterbalance between the shape magnetic anisotropy, the magnetoelastic anisotropy, and the stress-annealing-induced anisotropy determines the hysteresis loops modification observed in Figures 7 and 8.
In terms of the core-shell domain structure model, the modification in remanent magnetization, M r /M o , along the microwire can be attributed to the change in the inner axially magnetized core radius, R c , considering its relationship with M r /M 0 , given as [27,73,74]: where R is the metallic nucleus radius. Accordingly, the observed spatial distribution of hysteresis loops must be attributed to a gradual modification of the domain structure along the length of the microwires stress-annealed in a temperature gradient.
Coexistence of double-peak ∆Z/Z(H) dependencies and rectangular bulk hysteresis loops in stress-annealed Co-rich microwires has been explained considering the frequency dependence of the skin penetration depth, δ, as well as the existence of thin surface layers with circumferential magnetic anisotropy [48,49,83]. At relatively low frequencies, the skin depth is comparable and even higher than the microwire radius, and therefore, the current flows through the whole ferromagnetic nucleus. However, as the frequency rises, the current flows closer to the surface [83].
Therefore, the modification of a magnetic domain structure upon stress-annealing consists of a change in the volume of the outer domain shell with circumferential magnetization orientation at the expense of the inner axially magnetized core.
Previously, a much more sophisticated technology involving a change in the chemical composition during deposition was proposed to obtain thin films with graded magnetic anisotropy [54,55]. Magnetic materials with graded properties have been proposed for various applications, including magnetic recording, manipulations of electromagnetic waves, or controllable domain wall propagation [54][55][56][57]85,86]. Thus, recently, controllable domain wall-breaking or -trapping have been reported for Fe-rich magnetic microwires with graded magnetic anisotropy [57].
The influence of various parameters, such as annealing temperature, applied stress during annealing, or annealing time on the magnetic anisotropy of Co-rich microwires with vanishing magnetostriction was recently demonstrated by us in several publications [49][50][51]82]. The only parameter that can be easily changed during the same experiment is the annealing temperature. We previously used this solution for the preparation of Fe-rich microwires with graded magnetic anisotropy. Accordingly, we selected Co-rich microwires of two different compositions and geometries to prove that, as with Fe-rich microwires, such processing can be used to obtain Co-rich microwires with graded magnetic anisotropy.
Obtained Co-rich microwires with gradual sensibility to magnetic fields are suitable for the development of magnetic sensors capable of detecting both a magnetic field and its approximate location along the microwire length. For example, the dependence of the sample magnetization measured in a given magnetic field versus their position along the sample may be suitable for position sensors. Additionally, the studied samples have been shown to exhibit excellent magnetic softness, and hence can be good candidates for GMI-related technologies, as magnetic softness has been reported to be related to high GMI effectiveness. On the other hand, thick Co-rich microwires with tunable harmonics can be useful for various applications, such as security and electronic surveillance or smart composites for non-destructive control applications. Stress-annealing-induced magnetic anisotropy is a useful tool for improvement of the stress sensitivity of the magnetic properties of magnetic microwires [87]. Therefore, the use of Co-rich microwires with graded magnetic anisotropy is expected to improve the performance of stress-sensitive composites with microwire inclusions.
Accordingly, we propose a rather simple route involving stress-annealing in a temperature gradient to design graded magnetic anisotropy in Co-rich magnetic microwires.

Conclusions
In this paper, we proposed a rather simple method for preparation of Co-rich microwires with graded magnetic anisotropy consisting of stress-annealing under a temperature gradient. A gradual change in the hysteresis loop of a Co-rich glass-coated microwire stress-annealed at variable temperature was observed. Additionally, such microwires stress-annealed with a temperature gradient also presented with a variable squareness ratio and magnetic anisotropy field along the microwire length. Obtained graded anisotropy has been attributed to a gradual modification of the domain structure along the microwire originated by a counterbalance between shape, magnetoelastic, and induced magnetic anisotropies. The gradual sensibility to magnetic fields would allow for the development of magnetic sensors capable of detecting both a magnetic field and its approximate location along the microwire length. Studied samples have shown to exhibit excellent magnetic softness, and hence can be a good candidate for GMI-related technologies, as magnetic softness has been reported to be related to high GMI effectiveness. On the other hand, thick microwires with tunable harmonics can be useful for security and electronic surveillance and for non-destructive control applications.